Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C17 ⋊ #1939 |
260 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2176 |
Polycyclic presentation:
2^7,17|a^2=f,b^2=f,c^2=e,f^2=g,b^a=bd,c^a=ce,h^a=h^4,h^b=h^13,h^c=h^16,h^f=h^16136 conjugacy classes — view the full character table.
| maximal subgroup of | #17970419, C2×#14544883, #17970425, … |
| maximal normal subgroup of | #17970419, C2×#14544883, #17970425, … |
| maximal quotient of | #17955814, #17955817, #17955820, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 20609);